Proceedings of the 3rd International Conference on Mathematical Statistics and Economic Analysis, MSEA 2024, May 24–26, 2024, Jinan, China

Research Article

Mathematical Modeling of an Economic Cycle Model with Harmonic and Random Drivers

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  • @INPROCEEDINGS{10.4108/eai.24-5-2024.2350198,
        author={Jun  Zhao and Lingxi  Wu and Yang  Lu and Yu  Zhang and Huimei  Liu},
        title={Mathematical Modeling of an Economic Cycle Model with Harmonic and Random Drivers},
        proceedings={Proceedings of the 3rd International Conference on Mathematical Statistics and Economic Analysis, MSEA 2024, May 24--26, 2024, Jinan, China},
        publisher={EAI},
        proceedings_a={MSEA},
        year={2024},
        month={10},
        keywords={mathematical modeling economic cycle model harmonic adjustment uncertainty},
        doi={10.4108/eai.24-5-2024.2350198}
    }
    
  • Jun Zhao
    Lingxi Wu
    Yang Lu
    Yu Zhang
    Huimei Liu
    Year: 2024
    Mathematical Modeling of an Economic Cycle Model with Harmonic and Random Drivers
    MSEA
    EAI
    DOI: 10.4108/eai.24-5-2024.2350198
Jun Zhao1,*, Lingxi Wu1, Yang Lu1, Yu Zhang1, Huimei Liu1
  • 1: Tianjin Foreign Studies University
*Contact email: zhaojun@tjfsu.edu.cn

Abstract

Applied mathematics has been widely applied in various fields of science and engineering. Among these applications, the study of economic cycles is a very important branch. It is because that an economic system usually develops in a repetitive manner of expansion and contraction under many deterministic and random factors. It exhibits a complex phenomenon of nonlinearity and randomness. In this paper, a nonlinear economic cycle model is proposed to consider government adjustment and market uncertainty. The periodic income adjustment from government is applied to the model as a harmonic function with income. Meanwhile, Gaussian white noise is employed to model market uncertainty. The response of the nonlinear economic cycle model is investigated on its probability density function (PDF) using a path integral method. The short-time Gaussian approximation technique is introduced to evaluated the transition PDF between the two successive time intervals, and the Gauss-Legendre integration scheme is applied to the path integration. Two cases are considered in the following analysis. One is about the high-level government adjustment. The other is about the high-level market uncertainty. The results show that the joint PDF of income and income growth rate will reach a stable state and it periodically evolve along with time.